A punishment inflicted by private soldiers on their comrades for trifling offences, or breach of their mess laws; it is administered in the following manner: The prisoner is set against the wall, with the arm which is to be burned tied as high above his head as possible. The executioner then ascends a stool, and having a bottle of cold water, pours it slowly down the sleeve of the delinquent, patting him, and leading the water gently down his body, till it runs out at his breeches knees: this is repeated to the other arm, if he is sentenced to be burned in both.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Cold * Cold CookNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes